Mixing solid copper, $5\%$ vinegar, and hydrogen peroxide ($\ce{H2O2}$) causes copper acetate to form. The process will occur very slowly without hydrogen peroxide. Adding $\ce{H2O2}$ speeds the formation of copper acetate.
How can I test the solution to see if all of the acetic acid has been converted into copper acetate?
If possible, provide answers that employ only household items or readily available devices.
Your question and title do not correspond, IMHO. I'll answer one of both:
Vinegar is mostly water, with some acetic acid ($5\%$). A classic experiment, performed by a lot of kids at school, is to mix vinegar with baking soda. The baking soda neutralizes the acid and produces carbon dioxide. The carbon dioxide is what you're looking for: it's the sign that the reaction is taking place.
Pour a pinch of baking soda inside your solution. If it makes bubbles on contact, your solution still contains a lot of vinegar. If you don't see any bubbles, even when stirring, most of the acid has been consumed.
